Following the derivation of the relations of incremental stresses and strains for an idealized fiber-reinforced isotropic elastic material, the instability problem stated in the title is analyzed on the basis of Biot’s mechanics of incremental deformations. The analysis indicates that the slab reinforced by fibers along the direction of its thickness under axial loads becomes unstable in a manner different from the case of an unreinforced slab. In the course of the analysis the material was specified as the so-called Blatz-Ko rubber, solid and foam. It was found that the slab of solid rubber buckled only under compression, while that of foam rubber became unstable under tension as well as under compression. There exist two types of buckling for foam rubber under tension: a shear buckling and an internal buckling. However, the latter does not manifest itself physically since the former always occurs first.

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